Firstly if you're trading daily, it should be a reasonable assumption that you're signal isn't too quick. So if you backtested getting your fill at the next days close, how much does it degrade your Sharpe Ratio? If by more than 20% then you're probably using signals too quick for daily prices, closing or otherwise. A moving average crossover of at least 3,12 should be fine.
Okay so lets assume daily prices are fine.
Close prices can also be "odd". Ideally you can trade once a day and not use EOD data (this is pretty close to what I do). So for example you'd come into the market once a day, get your price, calculate your trade, and then go into the market. I'd then issue a limit order on the correct side of the spread, and if that doesn't work out cross the spread
(heres what I do in practice). If you don't want to manage the trade then issue a market order or a limit order which crosses the spread immediately.
If you have to use closing prices then the key decision is how you should react to movements between the close and where prices are on the open or might be when you get filled. If you're using moving average crossover, I guess you're trend following. Suppose your signal is positive. So if the price has moved up you'll still want to buy, probably even more. If the price has moved down would you still want to buy? If you updated your system with the new price would it still want to buy? It's possible, though hard work, to do calculations of the kind of 'here is the range in which I'd still want to buy' and then issue orders that reflect that.
Alternatively taking the view that you've simulated your system with a 24 hour delay and it still worked, you could take the view that your forecast is still for a trend based on the close, and you're just getting lucky with your fill on a slight pull back on a multi day trend. So again issuing an order based on the current price is probably fine.
On the other hand if you're trading mean reversion, or if you have got some concept of 'value in the trade' (i.e. due to pre determined exit prices) then you'd probably be happy if the price has dipped, and have some upper limit on what you'd be prepared to buy if the price has fallen.
